Annals of Global Analysis and Geometry

, Volume 23, Issue 1, pp 77–92

New Proof of the Cheeger–Müller Theorem


  • Maxim Braverman
    • Department of MathematicsNortheastern University

DOI: 10.1023/A:1021227705930

Cite this article as:
Braverman, M. Annals of Global Analysis and Geometry (2003) 23: 77. doi:10.1023/A:1021227705930


We present a short analytic proof of the equality between the analytic and combinatorialtorsion. We use the same approach as in the proof given by Burghelea, Friedlander andKappeler, but avoid using the difficult Mayer-Vietoris type formula for the determinantsof elliptic operators. Instead, we provide a direct way of analyzing the behaviour of thedeterminant of the Witten deformation of the Laplacian. In particular, we show that thisdeterminant can be written as a sum of two terms, one of which has an asymptoticexpansion with computable coefficients and the other is very simple (no zeta-functionregularization is involved in its definition).

Ray–Singeranalytic torsion

Copyright information

© Kluwer Academic Publishers 2003